Introduction to Get Set for Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

How to Answer Test Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

UnIT 1 The number System 9

8.NS.1 Lesson 1 Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 8.NS.2 Lesson 2 Irrational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

UnIT 2 Expressions and Equations 19

8.EE.1 Lesson 3 Laws of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 8.EE.2 Lesson 4 Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.EE.3 Lesson 5 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 8.EE.3, 4 Lesson 6 Operations with Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 8.EE.5, 6 Lesson 7 Proportional Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 8.EE.6 Lesson 8 Graphing Linear Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 8.EE.7 Lesson 9 Solving Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 8.EE.8.a, b Lesson 10 Systems of Linear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 8.EE.8.c Lesson 11 Problem Solving with Systems of Equations . . . . . . . . . . . . . . . . . . . 57

UnIT 3 Functions 63

8.F.1, 2 Lesson 12 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 8.F.2, 3, 5 Lesson 13 Graphs of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 8.F.3, 4 Lesson 14 Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

UnIT 4 Geometry 81

8.G.1, 3 Lesson 15 Translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 8.G.1, 3 Lesson 16 Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.G.1, 3 Lesson 17 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 8.G.3 Lesson 18 Dilations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 8.G.2, 4 Lesson 19 Congruency and Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 8.G.5 Lesson 20 Angle Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.G.6, 7 Lesson 21 The Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 8.G.8 Lesson 22 Finding Distance Between Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 8.G.9 Lesson 23 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

UnIT 5 Statistics and Probability 135

8.SP.1 Lesson 24 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 8.SP.2, 3 Lesson 25 Lines of Best Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 8.SP.4 Lesson 26 Two-Way Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Flash Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

T fa lb e Co t tn n seo

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Focus LessonA two-way table shows the frequency, or count, of two variables of data. One variable of data is displayed in the rows. The other variable is displayed in the columns.

To construct a two-way table, identify the two variables that represent the related pieces of data. Label the rows using one of the variables. Label the columns using the other variable.

Relative frequencies can be computed from the frequencies in a two-way table. Relative frequency is the fraction of times a data value occurs. To find relative frequency, divide each frequency by the total count in the data. Relative frequencies can be written as fractions, decimals, or percents.

In a survey, responders were asked if they have pets at home and if they watch a certain television show about pets. The table below shows the results of the survey.

PET SURVEY

Watch Show About Pets

Do Not Watch Show About Pets

Have a Pet 8 33

Do Not Have a Pet 3 16

Based on the table, what percent of responders surveyed have a pet but do not watch the show about pets?

________ %

1  Describe in words how to find the number of responders who have a pet but do not

watch the show about pets. _____________________________________________________

______________________________________________________________________________

2 How many responders have a pet but do not watch the show about pets? ________

3 What is the total number of responders in this survey? ________

4 Write an expression to use to find the relative frequency of responders who have a pet

but do not watch the show about pets. ________________

What percent of responders surveyed have a pet but do not watch the show about pets?

Lesson 26 two-Way tables

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Guided Practice

Emily asked all the eighth graders in her school whether they play an instrument or take a foreign language. The results of her survey are shown in the table below.

SURVEY RESULTS

Take a Foreign Language

Do Not Take a Foreign Language

Play an Instrument 64 8

Do Not Play an Instrument

31 35

Emily made a reasoned conclusion from the data. Circle an option in each set that most accurately completes the following statement about Emily’s conclusion.

Based on the table, eighth graders that [ do, do not ] play an instrument are [ less likely,

more likely ] to take a foreign language.

1 About what percent of the students that play an instrument also take a foreign language—significantly less than 50%, about 50%, or significantly more than 50%?

________________________________________________

2 About what percent of the students that do not play an instrument also take a foreign language—significantly less than 50%, about 50%, or significantly more than 50%?

________________________________________________

Which option in each set completes the statement about Emily’s conclusion?

How many total eighth graders play an

instrument?

Is there a significant difference in the frequencies for students that do not play an instrument?

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Independent Practice

Solve the following problems.

1 The table below shows some characteristics of students in Mr. Lanning’s class.

STUDENT CHARACTERISTICS

Has Brown Hair

Does Not Have Brown Hair

Girl 9 5

Boy 6 3

How many students are in Mr. Lanning’s class?

________

2 Students and teachers at Alex’s school were surveyed about whether or not they want to change the school’s mascot. The results of the survey are shown in the table below.

MASCOT SURVEY RESULTS

Change Mascot Do Not Change Mascot

Students 318 428

Teachers 15 55

Based on the results of the survey, which statement is true? Select all that apply.

A A total of 746 people were surveyed.

B A total of 70 teachers were surveyed.

C Of the teachers surveyed, 55 do not want to change the mascot.

D Of the students surveyed, 318 do not want to change the mascot.

E More than twice as many teachers do not want to change the mascot than do want to change it.

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Independent Practice

3 Two of the activities a camp offers its campers are kayaking and horseback riding. The table below shows the number of campers taking these activities.

CAMP ACTIVITIES

Take Horseback Riding

Do Not Take Horseback Riding

Take Kayaking 11 12

Do Not Take Kayaking

18 4

What fraction of campers takes only one of these activities?

 

4 Claudia recorded the ages and asking prices of used cars in the classified section of a newspaper. The table below shows the data Claudia recorded.

USED CAR PRICES

AG

E O

F C

AR

Less than $5,000

From $5,000 to $7,500

From $7,501 to $10,000

More than $10,000

Less than 2 Years 0 0 2 12

From 2 to 5 Years 0 0 3 6

From 6 to 10 Years 5 3 3 1

More than 10 Years

4 0 0 1

Based on the data in the table, which of the following conclusions can be made? Select all that apply.

A All used cars older than 10 years cost less than $5,000.

B All used cars less than 2 years cost more than $7,500.

C More used cars are less than 2 years old than are 2 years old or greater.

D More used cars are 5 years old or less than are greater than 5 years old.

E As the age of the car increases, the price of the car tends to increase.

F As the age of the car increases, the price of the car tends to decrease.

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Independent Practice

5  Dante recorded the colors and types of vehicles parked in the teacher’s parking lot at school one day. Listed below is the data Dante recorded.

•  There are exactly 56 vehicles.•  The colors of the vehicles are: red, black, white, blue, and green.•  The types of vehicles parked are: cars, SUVs, and trucks.•  The colors of the cars are: 9 red, 13 black, 7 white, 4 blue, and 2 green.•  There are 10 SUVs in the lot, the same number of each color. •  The colors of all vehicles are: 15 red, 18 black, 10 white, 9 blue, and 4 green.

Fill in the data in the empty table below to show the number of each color and vehicle type that is parked in the teachers’ parking lot.

TEACHERS’ PARKING LOT

Cars SUVs Trucks

Red

Black

White

Blue

Green

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